How do you find the derivative of #f(x) = log_x e#? Calculus Differentiating Logarithmic Functions Differentiating Logarithmic Functions without Base e 1 Answer Jim H Apr 10, 2016 Use change of base to write #f(x) = lne/lnx = 1/lnx = (lnx)^-1# Explanation: So #f'(x) = -(lnx)^-2 (1/x) = (-1)/(xln^2x)# Answer link Related questions What is the derivative of #f(x)=log_b(g(x))# ? What is the derivative of #f(x)=log(x^2+x)# ? What is the derivative of #f(x)=log_4(e^x+3)# ? What is the derivative of #f(x)=x*log_5(x)# ? What is the derivative of #f(x)=e^(4x)*log(1-x)# ? What is the derivative of #f(x)=log(x)/x# ? What is the derivative of #f(x)=log_2(cos(x))# ? What is the derivative of #f(x)=log_11(tan(x))# ? What is the derivative of #f(x)=sqrt(1+log_3(x)# ? What is the derivative of #f(x)=(log_6(x))^2# ? See all questions in Differentiating Logarithmic Functions without Base e Impact of this question 1260 views around the world You can reuse this answer Creative Commons License